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\begin{equation*}(\mathbf{ij})^2 = (\mathbf{ij})(\mathbf{ij}) = \mathbf{i}(\mathbf{j}\mathbf{i})\mathbf{j} = \mathbf{i}(\mathbf{i}\mathbf{j})\mathbf{j} = (\mathbf{ii})(\mathbf{jj}) = \mathbf{i}^2\mathbf{j}^2\end{equation*}
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